Mesh is having trouble following bones correctly
Your "pirate" head looks better in my blender:



but the head, at least, moves wrongly because you are not seeing bones axis rotation, in stick mode: try octahedron mode:



but I also inspected weight influences, and some bones have slight influence on the head, too, so do a complete check again, maybe.

I always reccomend to get help from custom weight paint color to help visualize difficult wrong spots...



see this other old (my) answer about it: When IK bone moved wrong part of mesh deforms